Galois group: 24T2680

• Label: 24T2680
• Degree: $24$
• Order: $1152$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• $p$-group: no
• Group: $C_{12}^2:D_4$

Group invariants

Abstract group:		$C_{12}^2:D_4$
Order:		$1152=2^{7} \cdot 3^{2}$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$24$
Transitive number $t$:		$2680$
Parity:		$-1$
Primitive:		no
$\card{\Aut(F/K)}$:		$6$
Generators:		$(1,19,5,24,4,21,2,20,6,23,3,22)(7,13,11,17,10,16,8,14,12,18,9,15)$, $(1,18,10,22,2,17,9,21)(3,14,11,23,4,13,12,24)(5,15,8,19,6,16,7,20)$, $(1,9)(2,10)(3,12)(4,11)(5,7)(6,8)(13,15,18,14,16,17)(19,22,23,20,21,24)$

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$ x 7
$3$:	$C_3$
$4$:	$C_2^2$ x 7
$6$:	$S_3$, $C_6$ x 7
$8$:	$D_{4}$ x 6, $C_2^3$
$12$:	$D_{6}$ x 3, $C_6\times C_2$ x 7
$16$:	$D_4\times C_2$ x 3
$18$:	$S_3\times C_3$
$24$:	$S_3 \times C_2^2$, $(C_6\times C_2):C_2$ x 6, $D_4 \times C_3$ x 6, 24T3
$32$:	$C_2^2 \wr C_2$
$36$:	$C_6\times S_3$ x 3
$48$:	24T25 x 3, 24T38 x 3
$64$:	$(((C_4 \times C_2): C_2):C_2):C_2$
$72$:	12T42 x 6, 24T68
$96$:	24T112, 24T116
$128$:	$C_2 \wr C_2\wr C_2$
$144$:	24T248 x 3
$192$:	24T286, 24T334
$288$:	24T626
$384$:	24T713, 24T714

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 3: None

Degree 4: $D_{4}$

Degree 6: $S_3\times C_3$

Degree 8: $C_2 \wr C_2\wr C_2$

Degree 12: 12T42

Low degree siblings

24T2680 x 15

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

Conjugacy classes not computed

Character table

135 x 135 character table

Regular extensions

Data not computed